Doing the double this season was always going to be a long shot for Leicester City and there is no chance of it now. Tottenham Hotspur, on the other hand, remain in the hunt for success on multiple fronts, and the manner of this victory can only have increased the confidence around the club. This was a powerful demonstration of the strength of Spurs’ squad and of the size of the challenge facing Colchester United in the fourth round.

Both managers made eight changes to their line-ups from their last Premier League outings, but Tottenham’s performance barely dipped. Superb goals from Son Heung-min and Nacer Chadli helped them secure a rather emphatic victory over Claudio Ranieri’s team – at last.

This was the clubs’ fourth meeting of the season and their third in 10 days, a quirk that prompted the King Power stadium announcer to tell the 3,000 travelling Tottenham fans before kick-off that “you lot are almost like family now”.

If that was the case, then Leicester came into the match as the daddies, enjoying a better position in the Premier League table and the upper hand in their clashes so far in the campaign: two draws and a victory. But it did not take long for Tottenham to establish their authority here.

Leicester were made to seem submissive. Their line-up may have been different but they stuck to what has become their usual pattern in recent weeks, allowing the opposition plenty of possession while seeking to counterattack in lightning bursts, though their capacity to do that was drastically reduced by the omission of Jamie Vardy and Riyad Mahrez.

Demarai Gray, the 19-year-old signed this month from Birmingham City, looked bright in glimpses. “He is a very good diamond but we have to work on him to help his light shine,” Ranieri said. But Spurs mostly obscured Leicester’s forwards by ensuring play was confined to the other end.

With Leicester defending en masse, it was 14 minutes before Spurs created a clear opportunity, but Christian Eriksen sliced way wide from the edge of the area after a cutting move down the left. Ten minutes later, Ben Davies missed by almost as much when a rehearsed corner routine presented him with a chance to shoot from 20 yards. Erik Lamela then missed the target with a header from a cross by Davies. With those being the only hints of danger at either end, the deadlock was already starting to look terminal.

In the 39th minute, however, Son ensured that Spurs’ initiative was rewarded. The Korean made space for a shot with a little shuffle that wrongfooted Ben Chilwell, the 19-year-old who otherwise made a fine home debut, before driving the ball past Kasper Schmeichel from 20 yards.

Now it was up to Leicester to attack but they could not get on to the front foot, as Spurs spent the remainder of the first half probing for a second goal.

Ranieri tried to make his side sharper for the second half by withdrawing Danny Drinkwater and introducing Shinji Okazaki and switching to 4-4-2. The dynamism of the Japan international almost led to an equaliser in the 53rd minute, when Okazaki, after pestering the Spurs defence, slipped the ball through to Nathan Dyer, whose curling shot from the left was tipped around the post by Vorm.

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Suddenly Leicester cranked into overdrive as they played with a zest and boldness unseen in the first period. Spurs were straining to keep the hosts at bay. Eager to reverse the flow, Mauricio Pochettino turned to Harry Kane on the hour; within two minutes Schmeichel had to beat away a 20-yard shot from the striker.

Spurs clinched victory in the 66th minute with a goal of exquisite class. Kane popped the ball to Son, who dissected the Leicester defence with a precise ball into the path of Chadli. The Belgian slotted the ball expertly past the advancing Schmeichel.

Ranieri unleashed Vardy towards the end but a comeback never looked likely. “We showed we have a strong squad and can compete in every competition,” said Pochettino, who noted the identity of the scorers showed Spurs do not necessarily need to sign another forward this month to relieve the burden on Kane.

He said: “This was a good opportunity for Nacer and Son to show that they can score so we are very pleased. We can improve, yes, and if we find the right player, then OK, but if not, I am very happy with the squad that we have. We are at a fantastic level at the moment. I’m very pleased with the competition between our attacking players, very pleased with the balance in the squad.”

Ranieri insisted he was disappointed to exit the FA Cup but acknowledged that missing future rounds could have an upside in terms of the club’s Premier League challenge.

“Now I can give my players one or two days more off to recover, because we are spending a lot of energy in every match,” he said.